107 LearnersLast updated on May 26th, 2025
Cube Root of 819
A number multiplied by itself three times to produce the original number is its cube root. Cube roots have practical applications in fields such as architecture and material science. We will now find the cube root of 819 and explain the methods used.
What is the Cube Root of 819?
We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓.
In exponential form, ∛819 is written as 819(1/3). The cube root is the inverse operation of finding the cube of a number. For example, assume 'y' as the cube root of 819, then y3 can be 819. Since the cube root of 819 is not an exact whole number, we can write it as approximately 9.343.
Finding the Cube Root of 819
Finding the cube root of a number involves identifying the number that, when multiplied by itself three times, results in the target number. Various methods can be used to find the cube root of 819:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
To find the cube root of a non-perfect cube number like 819, Halley’s method is often used.
Cube Root of 819 by Halley’s method
Let's find the cube root of 819 using Halley’s method.
The formula is: ∛a ≅ x((x3 + 2a) / (2x3 + a)),
where: a = the number for which the cube root is being calculated
x = the nearest perfect cube
Substituting, a = 819;
x = 9
∛a ≅ 9((93 + 2 × 819) / (2 × 93 + 819))
∛819 ≅ 9((729 + 2 × 819) / (2 × 729 + 819))
∛819 ≅ 9.343
The cube root of 819 is approximately 9.343.
Common Mistakes and How to Avoid Them in the Cube Root of 819
Calculating the cube root of a number accurately can be challenging for students. Here are common mistakes made and ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Students often try to calculate an exact whole number for the cube root of numbers like 819, which are not perfect cubes.
For example, they might expect an exact whole number like they would for 729 (since ∛729 = 9). To avoid this error, memorize that some numbers don't have a perfect cube root. The cube root of 819 is approximately 9.343.
Cube Root of 819 Examples:
Problem 1
Imagine you have a cube-shaped storage container with a total volume of 819 cubic meters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛819 ≈ 9.343 meters
Explanation
To find the side of the cube, we need to find the cube root of the given volume.
Therefore, the side length of the cube is approximately 9.343 meters.
Problem 2
A warehouse contains 819 cubic meters of sand. Calculate the amount of sand left after using 200 cubic meters.
The amount of sand left is 619 cubic meters.
Explanation
To find the remaining sand, subtract the used sand from the total amount: 819 - 200 = 619 cubic meters.
Problem 3
A tank holds 819 cubic meters of water. Another tank holds a volume of 100 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 919 cubic meters.
Explanation
Add the volume of both tanks: 819 + 100 = 919 cubic meters.
Problem 4
When the cube root of 819 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 9.343 = 28.029 The cube of 28.029 ≈ 22000.3
Explanation
Multiplying the cube root of 819 by 3 results in a significant increase in volume since the cube increases exponentially.
Problem 5
Find ∛(400 + 419).
∛(400 + 419) = ∛819 ≈ 9.343
Explanation
As shown in the question ∛(400 + 419), we simplify by adding them: 400 + 419 = 819.
Then calculate ∛819 ≈ 9.343 to get the answer.
FAQs on 819 Cube Root
1.Can we find the Cube Root of 819?
2.Why is Cube Root of 819 irrational?
3.Is it possible to get the cube root of 819 as an exact number?
4.Can we find the cube root of any number using prime factorization?
5.Is there any formula to find the cube root of a number?
Important Glossaries for Cube Root of 819
- Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.
- Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. A perfect cube always results in a whole number. For example, 2 × 2 × 2 = 8, therefore, 8 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a^(1/3), ⅓ is the exponent which denotes the cube root of a.
- Radical sign: The symbol used to represent a root, expressed as (∛).
- Irrational number: Numbers that cannot be expressed as a simple fraction are irrational. For example, the cube root of 819 is irrational because its decimal form goes on continuously without repeating the numbers.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
